The lowest, or most negative, palindrome I found is (4-6)^5 + (5-9)^1 + (2-8)^7 = -279,972. The highest, or least negative, is of course -1, with (1-2)^3 + (3-4)^5 + (6-7)^8 as one way to get it.

The lowest tautonymic I found is (1-4)^6 + (6-8)^3 + (2-9)^7 = -822,822. And for the highest tautonymic, one of several ways to get -1010 is (2-6)^5 + (5-3)^4 + (7-9)^1.

Looking at the earlier Palindromic and Tautonymic problem, I can't help but wonder if the equation for this problem should really be (A-B)^C + (D-E)^F + (G-H)^I, and it would be interesting to see what the results of that would be ...